To achieve faster scanning along a 3D trajectory we coupled to our two-photon microscope (Femto2D, Femtonics) a rapid cylindrically symmetric piezoelectric actuator (Physik Instrumente, Karlsruhe, Germany) with high resonant frequency (~ 1100 Hz without load) and used 100-700 Hz sine wave driving signal (Katona et al., 2011). Speeding up the driving
frequency of the piezo-positioner from the earlier described 10 Hz leads not just to a drop in amplitude and change in phase of the sinusoid movement (Gobel et al., 2007), but also resulted in a profound deviation of the position function from the sine wave (Figure 4A). We maintained a resonance in the objective movement without servo feedback, whilst measuring the position signal. After 50-100 cycles the movement of the objective reached a steady-state response function z(t) at a mean position (Figure 4B). We measured this non-linear z(t) function to generate a drive signal for the xy deflection (Figure 4C). First, using the z(t) response function, the t1 time was determined when the focal plane of the objective was at height z1, z(t1)=z1, (Figure 4 Ca and Cb), then at this t1 time point the xy drive signal for the galvanometer scanner was set to (x1, y1) to fit the 3D trajectory f(x1,y1,z1) (Figure 4 Cc). This process was repeated for the remaining points of the entire 3D trajectory selected for measurement.
We wrote software elements to help the fast orientation in 3D space, the selection of the 3D trajectories according to the stacks and the optimal utilization of the whole available z-scanning range. Namely, after acquisition of a z-stack, the recorded image series were used to aid the selection of the 3D path by scrolling through without scanning using the focusing handwheel of the microscope (rotary encoder; M101B, Megatron) for z and the computer mouse for xy coordinate settings. The selected 3D trajectory was the result of an interpolation algorithm which was based on guide points selected on the image stack of the chosen dendritic region. We named this method Roller Coaster Scanning (Katona et al., 2011) according the similarity in the movement trajectories.
The stability of the 3D trajectory scanning was verified by bleaching 3D curves in a homogeneous fluorescent plastic sample. A z-stack of the fluorescence was taken afterwards, and inverted, representing the time-averaged laser irradiation in the 3D space.
When scanning a trajectory with 150 Hz (the same as in Figure 5A) shows that the trajectory was followed at high precision in all dimensions (Figure 4D). When scanning with a much higher speed at the resonance peak around 700 Hz, the resulting bleached trajectory deviates significantly from the planned one (Figure 4E). However, the trajectory was stable;
suggesting that resonance might be better controlled with optimized mechanical design and/or with the use of software corrections. To compensate for deviations from the planned trajectory in the 150 Hz regime, we used a manual approach. We repeatedly moved the
points selecting the 3D trajectory in the xy plane while monitoring the basal fluorescence increase in the measured raw fluorescence traces until a better overlap between the 3D trajectory and the selected dendritic segment was visible.
Figure 4 Roller Coaster Scanning.
(A) The z-scanning range of the Roller Coaster Scanning as a function of repetition frequency.
Note the resonance peak at 690 Hz. (B) Diagram showing the z-position of the objective as a function of time within a single oscillation period after the oscillation has become stable. The nonlinearity of the response is only apparent at higher frequencies. (C) Principle of calculating the Roller Coaster Scanning movement. (Ca) After 50-100 cycles (warm up period) the position of the objective reached a steady-state nonlinear response function (z(t)), the amplitude of which was set to be larger than the required z-scanning range in imaging. (Cb) For each t1 time-point the location on the 3D trajectory was determined whose z coordinate equaled z(t ). (Cc) The x and y coordinate projections of the 3D trajectory (x, y )
determined the x(t) and y(t) functions which were used as command signal of the digital servo of the scanner motors. As illustrated in Cb, the descending and ascending phase of the oscillation could cover different parts of the selected 3D trajectory. (D) Maximum intensity image stack projection of an originally homogeneous fluorescent sample after bleaching it along the user-selected 3D trajectory also used in Figure 5A and B. Measured intensities were inverted. User-selected 3D trajectory is overlaid in red. (E) The same measurement, but at the 690 Hz resonance peak. Note that although the measured trajectory did not follow the user selected one, it was stable suggesting that software correction is possible. On D and E scale bars apply for all panels. (Katona et al., 2011)
We tested our method in biological measurements by scanning multiple spines of a CA1 hippocampal pyramidal cell simultaneously in 3D (Figure 5A) and by scanning long segments of dendrites of a CA1 interneuron (Figure 5B). Our approach resulted in a relatively limited, but biologically relevant z-scanning range (28 µm at 150 Hz, Figure 4A), while maintaining an advantageous FOV (650 x 650 µm2 with 20x objective) and resolution parameters characteristic of two-photon microscopy near the theoretical diffraction limit. Namely, we tested two objectives: in the case of XLUPlanFI 20x (Olympus) FWHM of the PSF is 450 nm in XY and 2400 nm in Z and with the LUMPlanFI/IR 60x (Olympus) FWHM of the PSF is 430 nm in XY and 2300 nm in Z. Resonation frequencies 120-200 Hz were used for the biological measurements.
To estimate a measure of the benefit of Roller Coaster Scanning in our conditions, we first constructed the length statistics of dendritic sections gained after cutting reconstructed dendritic trees into slices parallel to the focal plane (Figure 5C Inset). Then for a given slice thickness representing available z-range, we calculated the percentage of the dendritic sections being larger than a threshold, thus being appropriate for a virtual measurement (Figure 5C). To derive a simple number expressing the benefit of our new method, we compared the access rate of the ideal axial resolution grab condition to the 7 - 25 µm z-grab conditions used in our experiments at the mean segment length of dendrites imaged in our study (42.3 ± 7.4 μm; range, 10–250 μm). The geometric mean of the ratios representing the two extremes is approximately 27. This means that using Roller Coaster Scanning we had approximately 27 times larger chance to image 40 μm dendritic segments than it would be with 2D scanning approaches.
Figure 5 3D two-photon dendritic imaging at 150 Hz.
(Aa) 3D reconstruction of a CA1 pyramidal cell dendritic segment. The red curve shows the 3D trajectory of the scanning crossing the dendritic segment and spines. The blue box is 15 x 15 x 37 µm3. (Ab) Enlarged view of the blue box in Aa. A total of 18 regions including 12 spines located on the 3D scanning trajectory were measured simultaneously at 150 Hz. Ca2+
transients were induced by bAPs elicited by somatic current injection steps (5 APs, 35 Hz, average of 5 traces). (Ba) Maximum intensity side projection of a long CA1 interneuron dendrite. The pipette has been removed from the image. (Bb) 3D trajectory-scan measured along the dendrites in Ba. White open triangle indicates the time when bAPs were induced by somatic current injections (5 APs, 35 Hz, average of 5 traces). The horizontal axis is the spatial dimension along the measurement line (note that the scanning speed along the line is variable due to the nature of the Roller Coaster Scanning). Time is displayed along the vertical axis. (Bc) Relative fluorescence image (3D Ca2+ response) calculated from Bb.
Colorbar: 0-63 % ΔF/F. (Bd) Individual Ca2+ transients measured in the color coded regions in Bb (black bars indicate current injections). Note the high SNR. (C) Access rate of long dendritic segments for 3D scanning shown at three different z-scan ranges. (Inset) Lateral projection of six reconstructed CA1 stratum radiatum interneurons used for this statistical calculation (scale bar: 100 µm). (Katona et al., 2011)